Linear ProgrammingMathematical background; Theory of the simplex method; Detailed development and computational aspects of the simplex method; Further discussion of the simplex method; Resolution of the degeneracy problem; The revised simplex method; Duality theory and its ramifications; Transportation problems; Network flows; Special topics; Applications of linear programming to industrial problems; Applications of linear programming to economic theory. |
Contents
INTRODUCTION | 1 |
MATHEMATICAL BACKGROUND | 24 |
THEORY OF THE SIMPLEX METHOD | 71 |
Copyright | |
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a₁ activity vector artificial variables artificial vectors assume b₁ basic feasible solution basis matrix basis vectors branch capacity cells column components compute cone Consider contains convex combination convex set corresponding cost degeneracy denoted destination discussed dual problem dual variables enter the basis equations example extreme point finite number given Hence hyperplane identity matrix industry initial basic feasible iteration labeled linear programming problem linearly independent loop maximal flow minimum nodes non-negative Note objective function obtain optimal basic solution optimal solution path Phase player positive primal problem primal-dual algorithm procedure refinery removed restricted primal revised simplex method satisfied set of constraints set of feasible simplex algorithm slack variables surplus variables Table tableau tion transhipment transportation problem unbounded solution unique unit upper bound vector to enter yield zero level Zj Cj